Tensor decompositions [1]} give powerful tools to represent and compress higher-order arrays.
In this work, we focus on the symmetric rank-\(r\)  Tucker decomposition [2]}.
Applied to a \(d\) -th order symmetric tensor of size \(n \times \ldots \times n\) , it expresses the input using a
symmetric core tensor \({C}\in \mathbb {R}^{r \times \dots \times r}\)  \((r \ll n)\)  and a matrix \(\mathbf {Q}\in \mathbb {R}^{n \times r}\)  with orthonormal columns.
See fig: sym Tucker for an illustration.
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